The most dangerous slope angles for avalanches are between 30 and 50 degrees.

Statistically, 38° is the “oh-my-god-we’re-all-gonna-die slope”. An inclinometer is a useful tool to carry to help evaluate the potential of a particular slope. There’s no replacing hands-on training, but Bruce Temper’s Staying Alive in Avalanche Terrain is an excellent resource for learning more than you want to know about avalanches. (If you live in the northwest, you should give money to the Northwest Weather and Avalanche Center. They do good work.)